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One good way to do this type of problem is to shift your attention. Draw in the radii: OA, OB, QA,QB all of which you know. If you drop the circles you can then focus on the two isosceles triangles Note that E splits the chord AB so you know AE, EB. OQ is also perpendicular to AB. The key is shifting your attention towards the triangles: putting in the known pieces, then extracting the triangles. Walter Whiteley Michelle wrote back Walter: Thanks for your prompt reply. Regarding this question, the answer is square root of 7 + 3 square root of 3  which is how long OQ according to the answer in the back of the textbook. My question is how did they come up with that answer? Sincerely, Michelle Thanks for the compliment Michelle. Look at Walter's final diagram. QB is a radius of the circle centered at Q so the length of QB is 6. Since E splits the chord AB the length of EB is 3. Thus you know the lengths of two sides of the right triangle and by using the Pythagorian theorem you can find the length of the third side EQ. In a similar way you can find the length of OE. Is this what you tried? If you didn't get √7 + 3√3 what did you get? Penny
 


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